p^2=1p+42

Solution for p^2=1p+42 equation:

Simplifying
p2 = 1p + 42

Reorder the terms:
p2 = 42 + 1p

Solving
p2 = 42 + 1p

Solving for variable 'p'.

Reorder the terms:
-42 + -1p + p2 = 42 + 1p + -42 + -1p

Reorder the terms:
-42 + -1p + p2 = 42 + -42 + 1p + -1p

Combine like terms: 42 + -42 = 0
-42 + -1p + p2 = 0 + 1p + -1p
-42 + -1p + p2 = 1p + -1p

Combine like terms: 1p + -1p = 0
-42 + -1p + p2 = 0

Factor a trinomial.
(-6 + -1p)(7 + -1p) = 0

Subproblem 1
Set the factor '(-6 + -1p)' equal to zero and attempt to solve:

Simplifying
-6 + -1p = 0

Solving
-6 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1p = 0 + 6
-1p = 0 + 6

Combine like terms: 0 + 6 = 6
-1p = 6

Divide each side by '-1'.
p = -6

Simplifying
p = -6
Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve:

Simplifying
7 + -1p = 0

Solving
7 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1p = 0 + -7
-1p = 0 + -7

Combine like terms: 0 + -7 = -7
-1p = -7

Divide each side by '-1'.
p = 7

Simplifying
p = 7
Solution
p = {-6, 7}